1. If you have no connectivity, the app will frequently get stuck in the offline state, playing the spinner indefinitely, even after connectivity has returned. I had similar issues on Spotify, but Amazon Music is so much worse. 2. I had Amazon Music eat my entire cellular plan's data monthly allowance in a day, after it seemingly got stuck in a loop trying to download the same podcast again and again. The podcast is unplayable when it gets in this state, even on perfect Wi-Fi, it just never starts playback. This has happened twice now (incidentally on the same podcast, but different episodes), even after deleting and reinstalling the app entirely.
The second bug is a deal breaker, so I've gone back to Spotify.